1. Field of the Invention
The present invention relates to an apparatus for controlling a driving of an endless belt included in a color image forming apparatus to keep a linear velocity of the endless belt constant.
2. Description of the Related Art
As representative methods of forming a color image, there are a direct transfer system for transferring toner images of different colors formed on plural photoconductors directly onto transfer paper by superimposing the toner images, and an intermediate transfer system for transferring toner images of different colors formed on plural photoconductors onto an intermediate transfer unit by superimposing the toner images and thereafter collectively transferring the toner images onto transfer paper. These systems are called a tandem system since plural photoconductors are disposed opposite to the transfer paper or the intermediate transfer unit. An electrophotographic process of a formation of an electrostatic latent image and a development is carried out for each of yellow (Y), magenta (M), cyan (C), and black (K) colors for each photoconductor. According to the direct transfer system, toner images are transferred onto running transfer paper. According to the intermediate transfer system, toner images are transferred onto a running intermediate transfer unit.
A color image forming apparatus of the tandem system using the direct transfer system usually uses an endless belt that runs while supporting the transfer paper. A color image forming apparatus of the tandem system using the intermediate transfer system usually uses an endless belt that receives images from photoconductors and holds these images. Image forming units including four photoconductors are disposed on one running side of the belt. In the color image forming apparatus of the tandem system, superimposing the toner images of different colors in high precision is important for preventing a color drift. In both the transfer systems, to avoid a color drift due to a variation in the speed of the transfer conveyer belt, an encoder is fitted to one of driven axes of plural transfer units, and a rotation speed of a driving roller is feedback controlled according to the variation in the rotation speed of the encoder, as effective control means.
As one of the most general methods of realizing the feedback control, there is a proportional and integral control (PI control). According to the method, a position deviation e(n) is calculated based on a difference between a target angular displacement Ref(n) of the encoder and a detection angular displacement P(n−1) detected by the encoder. The result of the above calculation is lowpass filtered to remove high-frequency noise. A control gain is applied, and a constant standard driving pulse frequency is added, thereby controlling the driving pulse frequency of a driving motor connected to a driving roller. As a result, the encoder is always driven at a target angular displacement.
In the actual control, a counter that counts a rising edge of the output of an encoder pulse and a counter that counts each control period (for example, 1 millisecond) are used to obtain a position deviation from a difference between a calculation result of a target angular displacement that moves during the control period (1 millisecond) and a detection angular displacement that is obtained by acquiring the encoder count value during each control period. When a roller diameter of the driven axis to which the encoder is fitted is φ15.615, a detailed calculation is carried out as follows:e(n)=θ0×q−θ1×ne,where
e(n) [rad]: A position deviation (calculated at the sampling this time);
θ0 [rad]: A move angle per control period (=2π×V×10−3/15.565π [rad]);
θ1 [rad]: A move angle per one pulse of encoder (=2π/p [rad]);
q: A count value of control period timer; and
V: A belt linear velocity [mm/s].
Assume that a control period is 1 millisecond, and resolution of the encoder is 300 pulses per one rotation. A feedback control is carried out to operate the transfer conveyer belt at 162 mm/s. Then the move angles are obtained as follows:θ0=2π×162×10−3/15.615π=0.0207487 [rad]; andθ1=2π/p=2π/300=0.0209439 [rad].
The above calculation is carried out for each control period to obtain position deviations, thereby carrying out the feedback control.
The above method, however, has the following problems. The conveyance speed of the transfer paper changes due to a fine thickness of the conveyer belt. As a result, an image is deviated from an ideal position, which degrades the image quality. Images among plural sheets of recording papers vary, and repetitive positional reproducibility among the recording papers is degraded. When it is assumed that the conveyance speed is determined at the center of the belt thickness at the belt driving position, a belt conveyance speed V is calculated as follows:V=(R+B/2)×ω,where
R: Radius of the driving roller;
B: Thickness of the belt; and
ω: Angular velocity of the driving roller.
However, when a belt thickness B varies, a position of a belt thickness effective line shown in FIG. 21 changes. This is because a belt driving effective radius changes. It is clear that since (R+B/2) in the above expression changes, the belt conveyance speed changes even when angular velocity ω of the driving roller is constant. In other words, even when the driving roller is rotated at a constant angular velocity, the belt conveyance speed changes when the belt thickness varies.
FIG. 22 depicts a model of a belt driving conveyance system. FIG. 23 is a conceptual diagram of a variation in the belt thickness over full circle of the belt when the driving axis is rotated at a constant angular velocity and a variation in the belt conveyance speed. When a thick part of the belt is wound around the driving axis, a belt driving effective radius shown in FIG. 21 increases, and the belt conveyance speed increases. On the other hand, when a thin part of the belt is wound around the driving axis, the belt conveyance speed decreases.
FIG. 24 is a diagram for explaining a variation in the belt thickness on the driven axis and a variation in the belt conveyance speed detected in the driven axis when the belt is conveyed at a constant conveyance speed. Even when the belt is conveyed at an ideal speed without a speed variation, when a thick part of the belt is wound around the driven axis, a driven effective radius of the belt increases, and a rotation angular velocity of the driven axis decreases. This is detected as a decrease in the belt conveyance speed. When a thin part of the belt is wound around the driven axis, the rotation angular velocity of the driven axis increases, and this is detected as an increase in the belt conveyance speed. When the belt thickness varies in this manner, when a belt conveyance speed is detected in the rotation angular displacement of the driven axis in the encoder, an error detection component is generated. Therefore, even when the belt is conveyed at a constant speed, the belt conveyance speed is detected as if the speed is varying due to the variation in the belt thickness, in the detection of the rotation angular displacement of the driven axis. Therefore, according to the conventional feedback control of the driven axis, the variation in the belt thickness cannot be controlled.
As one of methods for solving the variation in the belt thickness, the following technique is known. When a driving roller is driven at a constant pulse rate, a speed profile that offsets a speed variation Vh that will occur due to a thickness profile over the whole peripheral direction of a known transfer conveyer belt is measured in advance, based on a position detected according to a belt mark. A driving motor control signal is generated at a modulated pulse rate. The motor is driven based on the generated signal. By driving the transfer conveyer belt via the driving roller, a final speed Vb of the transfer conveyer belt has no variation (see, for example, Japanese Patent Application Laid-Open No. 2000-310897).
However, speed profile data requires data for each control period. Therefore, when the control is carried out in a short period, a large capacity memory is necessary. When the control is carried out in a long period, sufficient effect cannot be obtained from the feedback control. When a belt length is 815 millimeters, when a belt driving speed is 125 mm/s, and when a control period is 1 millisecond, the belt speed is controlled by 6,520 times per one rotation of the belt as follows:815 mm/(125 mm/s×1 ms)=6520 times.
When a data size of the belt thickness per one point is expressed by 16 bits, a memory of 100 kilobits or more is necessary.6520 times×16 bit=104320 bit
Therefore, when the control is carried out using an actual device, a memory for storing a belt thickness profile is additionally necessary as a nonvolatile memory. Even when data is stored as compressed data and when the data is uncompressed in a volatile memory when the power source is turned on, a large capacity memory is necessary. Therefore, in addition to a memory used as a normal work area, a separate memory is necessary, which is unrealistic since the cost is substantially increased.
According to Japanese Patent Application Laid-Open No. 2000-310897, the belt thickness needs to be measured as profile data of the belt thickness. The thickness is measured with a laser displacement measuring device. The measured data is input at a product shipment time or by service personnel with an input unit such as an operation panel. However, to measure a variation in the belt thickness of a few micrometers, a high-precision measuring unit is necessary. Furthermore, since data management amount of the measured result and the data amount are large, input errors can occur.